Machine Learning Driven Forward Prediction and Inverse Design for 4D Printed Hierarchical Architecture with Arbitrary Shapes

Aug 3, 2026

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Forward prediction and inverse design for 4D printing have largely targeted 2D rectangular plates, leaving arbitrary-shaped 4D printed parts insufficiently studied due to difficulties in handling variable-sized inputs in machine learning pipelines. A machine learning-driven framework is proposed for 4D printed hierarchical architectures with arbitrary shapes by encoding non-rectangular geometries using special identifiers. Forward prediction is implemented with Residual Networks and inverse design with evolutionary algorithms, providing accurate and efficient performance, with low prediction loss and near-millimeter optimization error, validating the method for complex hierarchical structures.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages18

Reading Time45 min

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Introduction

Forward prediction and inverse design in 4D printing

Limitations of finite element analysis

Proposed hierarchical architectures and framework

Machine Learning Driven Forward Prediction and Inverse Design for 4D Printed Hierarchical Architecture with Arbitrary Shapes Liuchao Jina,b,c , Shouyi Yub,c , Jianxiang Chengb,c , Haitao Yec,d , Xiaoya Zhaie , Jingchao Jiangf, Kang Zhanga , Bingcong Jiang,b,c , Mahdi Bodaghih , Qi Geb,c,∗, Wei-Hsin Liaoa,i,∗ a Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Hong Kong, China b Shenzhen Key Laboratory of Soft Mechanics & Smart Manufacturing, Southern University of Science and Technology, Shenzhen, 518055, China c Department of Mechanical and Energy Engineering, Southern University of Science and Technology, Shenzhen, 518055, China d Department of Mechanical Engineering, City University of Hong Kong, Kowloon, Hong Kong, China e School of Mathematical Sciences, University of Science and Technology of China, Hefei, 230026, China f Department of Engineering, University of Exeter, Exeter, United Kingdom g School of Mechanical Engineering, Tongji University, Shanghai, 200092, China h Department of Engineering, School of Science and Technology, Nottingham Trent University, Nottingham, NG11 8NS, UKi Institute of Intelligent Design and Manufacturing, The Chinese University of Hong Kong, Hong Kong, China Abstract The forward prediction and inverse design of 4D printing have primarily focused on 2D rectangular surfaces or plates, leaving the challenge of 4D printing parts with arbitrary shapes underexplored. This gap arises from the difficulty of handling varying input sizes in machine learning paradigms. To address this, we propose a novel machine learning-driven approach for forward prediction and inverse design tailored to 4D printed hierarchical architectures with arbitrary shapes. Our method encodes non-rectangular shapes with special identifiers, transforming the design domain into a format suitable for machine learning analysis. Using Residual Networks (ResNet) for forward prediction and evolutionary algorithms (EA) for inverse design, our approach achieves accurate and efficient predictions and designs. The results validate the effectiveness of our proposed method, with the forward prediction model achieving a loss below 10−2 mm, and the inverse optimization model maintaining an error near 1 mm, which is low relative to the entire shape of the optimized model. These outcomes demonstrate the capability of our approach to accurately predict and design complex hierarchical structures in 4D printing applications. Keywords: 4D printing, machine learning, inverse design, hierarchical architecture, design optimization, residual network, evolutionary algorithm 1. Introduction 4D printing, an evolution of traditional 3D printing [1–5], has gained significant attention in the past decades due to its revolutionary potential in construction [6], textile [7, 8], automotive [9], aerospace industry [10], and biomedical applications [11–15] . Unlike conventional additive manufacturing processes that yield static objects, 4D printing empowers the creation of dynamic structures capable of self-transformation over time in response to external stimuli [16, 17], such as heat [18–24], light [25, 26], humidity [27, 28], pH [29, 30], and electric or magnetic fields [31–34] . Advances in 4D printing depend on the development of robust forward prediction and inverse design methods [35– 37] . Forward prediction involves predicting how a 4D-printed structure will behave when subjected to specific stimuli, such as temperature fluctuations, moisture absorption, or mechanical deformation [38] . In contrast, inverse design focuses on optimizing the material composition and structural configuration of a component to obtain predefined performance criteria or a desired response [39] . These two aspects of 4D printing design (forward prediction and ∗Corresponding authors Email addresses: [geq@sustech.edu.cn](geq@sustech.edu.cn) (Qi Ge), [whliao@cuhk.edu.hk](whliao@cuhk.edu.hk) (Wei-Hsin Liao) Preprint

FAQs

Why has inverse design for 4D printed arbitrary shapes been underexplored?

Existing work mainly focuses on 2D rectangular surfaces, and arbitrary shapes introduce challenges for machine learning due to varying input sizes.

How does the proposed method enable forward prediction for arbitrary-shaped hierarchical architectures?

It encodes non-rectangular geometries with special identifiers, then uses a Residual Network for forward prediction under prescribed stimuli.

What model is used for inverse design, and what optimization goal does it pursue?

An evolutionary algorithm is used for inverse design to optimize material composition and structural configuration so the structure achieves predefined performance criteria or desired responses.

Aug 3, 2026

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